Let `f(x)` be a polynomial of degree 5 such that `f(|x|)=0` has 8 real distinct , Then number of real roots of `f(x)=0` is ________.

Answer

5

Explanation

Since `f(|x|)=0` has 8 roots
`implies f(x)=0` has 4 real positive roots but since `f(x)` is polynomial of degree 5
`implies` fifth root is also real.
` :. ` Number of real roots of `f(x)=0` is 5